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Abstract – Central Point of the Thesis The paper proposes a unit-time-basis cost model for evaluating moving window joins. Using this cost model, it proposes strategies for maximizing the efficiency of processing joins in different scenarios. 4

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Background – Moving Window Join Instead of saying we want to join all tuples of A and B, we say we want to join all tuples that have arrived on A in the last t1 seconds with all the tuples that have arrived on S in the last t2 seconds. 11

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Introduction – Questions 1.How can we measure the efficiency of a moving window join evaluation strategy, since the traditional metric of execution time to completion does not apply? 2.Can an algorithm for a moving window join take advantage of asymmetries in the rates of the input streams? 3.How can we deal with cases in which an input stream is so fast that the system cannot keep up? 4.If memory is the bottleneck, how should we allocate memory between the two windows for the two inputs? 13

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Introduction – The Three Scenarios One stream is much faster than the other. System resources are insufficient to keep up with the input streams. Memory is limited. 14

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Cost of Nested Loop Join A to B 19 Number of tuples accessed in a time unit Cost of accessing a single tuple Number of tuples accessed to search for matched in window B Number of tuples insert and invalidation

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Cost of Hash Join A to B 20 Cost of probe(b) and invalidate(b) is a function of the hash bucket size in window B Cost of accessing a single tuple in a specific hash table implementation

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Observation from the Previous Graphs When input streams speed difference is minimal, HJ outperforms every other join combinations. As the speed gap increases, the cost of HJ increases considerably and exceeds that of HNJ at around 70 tuples/sec and 140 tuples/sec. Here we have a performance crossover point. 24

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Estimating the Weight Factors The crossover points can be calculated by equating the two cost formulas For two given streams, we can determine when NLJ will outperform HJ, depending on the ratio of the arrival of the input streams. 25 …

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Recall the three scenarios One stream is much faster than the other. System resources are insufficient to keep up with the input streams. Memory is limited. 27

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Exploiting Asymmetry in Input Streams Speed Assumptions: The two time windows are fixed. The aggregate speed of two streams is less than the systems service rate μ (i.e., λ a + λ b < μ ). The following inequality determines the likely winner between NLJ and HJ: If inequality holds, NLJ will outperform HJ; otherwise, HJ outperforms NLJ. 28

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Observation from the Previous Graphs HHJ costs the least until the input rate reaches about 70 tuples/sec; then HNJ takes over. Hence, either HHJ or HNJ is the winner. Both hash join output rates decrease drastically after passing their thrashing point. 30

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Maximizing the Number of Result Tuples with Limited Computing Resources This scenario arises under the following conditions: System evaluates very expensive predicates The input streams speed is faster than the join operators service rate, i.e., λ a + λ b > μ. Hence, not all answer tuples can be generated and input streams need to be regulated. But, what policy? 31

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Performance Comparison between Policies 32 The winner is the equal distribution strategy! Regardless of time window sizes and window selectivity factors.

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Maximizing the Number of Result Tuples with Limited Memory Assumption: The two time window sizes can be adjusted to fully utilize available memory. The two arrival rates are constant. Hence, memory allocation strategies are necessary. But, what policy? Will equal distribution win again? 33

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Performance Comparison between Policies 34 The winner is the Max A strategy, which allocates all memory to the slower stream. Keep the slower stream in memory and let the faster one probe against it and pass by.

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Maximizing the Number of Result Tuples with Limited Memory Another assumption: Variable time windows Variable arrival rates 35

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Performance Comparison between Policies 36 The best policy is either maximizing stream As time window in conjunction with maximizing Bs arrival rate, or we can maximize Bs time window and As arrival rate alternatively.

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Conclusion A unit-time basis model to analyze expected performance of moving window joins is introduced. The proposed cost-model divides the join cost into two independent terms, each corresponding to one of the two join directions. This work can be extended to have a cost model beyond single joins and for full query plans. Other algorithms apart from NLJ and HJ can be modeled and evaluated. 38